#curve25519 #ristretto #ristretto255 #crypto

no-std curve25519-dalek-fiat

A pure-Rust implementation of group operations on ristretto255 and Curve25519

1 unstable release

Uses old Rust 2015

0.1.0 Feb 16, 2021

#1118 in Cryptography

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Used in 136 crates (5 directly)


26K SLoC


curve25519-dalek-fiat on crates.io Documentation (latest release)


This is a thin fork of the curve25519-dalek project, authored by Isis Agora Lovecruft and Henry de Valence, in order to expose a formally verified backed end supplied by the fiat-crypto project, where primitive curve operations are extracted from Coq proofs of arithmetic correctness.

A pure-Rust implementation of group operations on Ristretto and Curve25519.

curve25519-dalek is a library providing group operations on the Edwards and Montgomery forms of Curve25519, and on the prime-order Ristretto group.

curve25519-dalek is not intended to provide implementations of any particular crypto protocol. Rather, implementations of those protocols (such as x25519-dalek and ed25519-dalek) should use curve25519-dalek as a library.

curve25519-dalek is intended to provide a clean and safe mid-level API for use implementing a wide range of ECC-based crypto protocols, such as key agreement, signatures, anonymous credentials, rangeproofs, and zero-knowledge proof systems.

In particular, curve25519-dalek implements Ristretto, which constructs a prime-order group from a non-prime-order Edwards curve. This provides the speed and safety benefits of Edwards curve arithmetic, without the pitfalls of cofactor-related abstraction mismatches.


To import curve25519-dalek-fiat, add the following to the dependencies section of your project's Cargo.toml:

curve25519-dalek-fiat = "0.1.0"

See CHANGELOG.md for more details.

Backends and Features

The nightly feature enables features available only when using a Rust nightly compiler. In particular, it is required for rendering documentation and for the SIMD backends.

Curve arithmetic is implemented using one of the following backends:

  • a fiat_u64_backend to use a verified u64 backend supplied by the fiat-crypto crate;
  • a u32 backend using serial formulas and u64 products;
  • a u64 backend using serial formulas and u128 products;
  • an avx2 backend using parallel formulas and avx2 instructions (sets speed records);
  • an ifma backend using parallel formulas and ifma instructions (sets speed records);

By default the u64 backend is selected. To select a specific backend, use:

cargo build --no-default-features --features "std fiat_u64_backend"
cargo build --no-default-features --features "std u32_backend"
cargo build --no-default-features --features "std u64_backend"
# Requires nightly, RUSTFLAGS="-C target_feature=+avx2" to use avx2
cargo build --no-default-features --features "std simd_backend"
# Requires nightly, RUSTFLAGS="-C target_feature=+avx512ifma" to use ifma
cargo build --no-default-features --features "std simd_backend"

Crates using curve25519-dalek can either select a backend on behalf of their users, or expose feature flags that control the curve25519-dalek backend.

The std feature is enabled by default, but it can be disabled for no-std builds using --no-default-features. Note that this requires explicitly selecting an arithmetic backend using one of the _backend features. If no backend is selected, compilation will fail.


The curve25519-dalek types are designed to make illegal states unrepresentable. For example, any instance of an EdwardsPoint is guaranteed to hold a point on the Edwards curve, and any instance of a RistrettoPoint is guaranteed to hold a valid point in the Ristretto group.

All operations are implemented using constant-time logic (no secret-dependent branches, no secret-dependent memory accesses), unless specifically marked as being variable-time code. We believe that our constant-time logic is lowered to constant-time assembly, at least on x86_64 targets.

As an additional guard against possible future compiler optimizations, the subtle crate places an optimization barrier before every conditional move or assignment. More details can be found in the documentation for the subtle crate.

Some functionality (e.g., multiscalar multiplication or batch inversion) requires heap allocation for temporary buffers. All heap-allocated buffers of potentially secret data are explicitly zeroed before release.

However, we do not attempt to zero stack data, for two reasons. First, it's not possible to do so correctly: we don't have control over stack allocations, so there's no way to know how much data to wipe. Second, because curve25519-dalek provides a mid-level API, the correct place to start zeroing stack data is likely not at the entrypoints of curve25519-dalek functions, but at the entrypoints of functions in other crates.

The implementation is memory-safe, and contains no significant unsafe code. The SIMD backend uses unsafe internally to call SIMD intrinsics. These are marked unsafe only because invoking them on an inappropriate CPU would cause SIGILL, but the entire backend is only compiled with appropriate target_features, so this cannot occur.


Benchmarks are run using criterion.rs:

cargo bench --no-default-features --features "std fiat_u64_backend"
cargo bench --no-default-features --features "std u32_backend"
cargo bench --no-default-features --features "std u64_backend"
# Uses avx2 or ifma only if compiled for an appropriate target.
export RUSTFLAGS="-C target_cpu=native"
cargo bench --no-default-features --features "std simd_backend"

Performance is a secondary goal behind correctness, safety, and clarity, but we aim to be competitive with other implementations. The new fiat_u64 backend incurs a 8-15% slowdown compared to the original u64 backend, depending on the EdDSA operation.

group ed25519_fiat_u64_backend ed25519_u64_backend
Ed25519 batch signature verification/128 1.10   3.0±0.01ms 1.00   2.7±0.01ms
Ed25519 batch signature verification/16 1.09   411.7±1.28µs 1.00   377.8±0.92µs
Ed25519 batch signature verification/256 1.09   5.4±0.01ms 1.00   4.9±0.01ms
Ed25519 batch signature verification/32 1.08   779.3±4.87µs 1.00   723.9±3.21µs
Ed25519 batch signature verification/4 1.09   137.9±0.75µs 1.00   127.0±0.30µs
Ed25519 batch signature verification/64 1.15   1590.2±44.34µs 1.00   1385.2±6.80µs
Ed25519 batch signature verification/8 1.09   229.0±0.92µs 1.00   210.2±0.63µs
Ed25519 batch signature verification/96 1.11   2.4±0.08ms 1.00   2.2±0.01ms
Ed25519 keypair generation 1.07   17.9±0.07µs 1.00   16.7±0.09µs
Ed25519 signature verification 1.11   51.1±0.26µs 1.00   46.1±0.29µs
Ed25519 signing 1.05   18.9±0.09µs 1.00   18.0±0.07µs
Ed25519 signing w/ an expanded secret key 1.11   18.6±0.13µs 1.00   16.8±0.13µs
Ed25519 strict signature verification 1.06   53.0±0.33µs 1.00   50.0±0.15µs


~41K SLoC